Question

How do simplify the fraction $\dfrac{15}{36}$ ?

Answer 1

Hint: In this problem we have to simplify the fraction of $\dfrac{15}{36}$. To simplify the fraction, we will consider both numerator and denominator separately and we will write the factors of both the numerator and denominator. After writing the factors we will write both numerator and denominator as products of the common factor of both the numbers. Now we will substitute those values in the given fraction and we will cancel the common term in both numerator and denominator then we will get the simplified form of the given fraction.

Complete step by step procedure:
Given that, $\dfrac{15}{36}$.
In the above fraction, we have the numerator as $15$ and the denominator as $36$.
Considering the numerator which is $15$. We have the factors of the number $15$ are $1$ , $3$ , $5$ , $15$. From the above factors we can write $15$ as
$15=1\times 15$,
$15=3\times 5$.
Considering the denominator which is $36$. We have the factors of the number $36$ as $1$, $2$, $3$, $4$, $6$, $9$, $12$, $18$, $36$. From the above factors we can write $36$ as
$36=1\times 36$,
$36=2\times 18$,
$36=3\times 12$,
$36=4\times 9$.
From the above values, we can write both numerator and denominator as the multiple of $3$.
 So, we are going to substitute the values of the numerator and denominator as $15=3\times 5$, $36=1\times 36$, then we will get
$\Rightarrow \dfrac{15}{36}=\dfrac{3\times 5}{3\times 12}$
Canceling the common factor $3$ in both numerator and denominator, then we will get
$\Rightarrow \dfrac{15}{36}=\dfrac{5}{12}$.

Hence the simplified form of the given fraction $\dfrac{15}{36}$ is $\dfrac{5}{12}$.

Note:
We can simplify any fraction up to we will get a prime number in either numerator or denominator. Because we don’t have any factors for the prime number, so there is a way to simplify the equation. In the above problem, we have got the numerator $5$ which is a prime number, so we have ended the procedure.